H∞ adaptive control for uncertain Markovian jump systems with general unknown transition rates

•The uncertain Markovian jump systems with GUTRs is investigated by adaptive control.•The uncertainties exist in not only parameters but also transition rates.•Each transition rate can be completely unknown or only its estimate value is known.•The derived results are less conservative than the conclusions recently presented in Applied Mathematical Modeling.

This paper investigates the H∞ adaptive control problem for uncertain stochastic nonlinear Markovian jump systems with general unknown transition rates (GUTRs). The uncertainties exist in not only parameters but also transition rates. Each transition rate can be completely unknown or only its estimate value is known. By constructing a new switching function, we design some robust controllers to guarantee the uncertain system subject to GUTRs is stochastically stable with a generalized H∞ disturbance attenuation level γ. The derived results are less conservative than the conclusions recently presented in Wang et al. (2011) [1]. In fact, the results in Wang et al. (2011) [1] is a special case of ours. Finally, a numerical example is presented to demonstrate effectiveness of the designed controller.